LTI-Discrete time System, Frequency Response, Fourier Transforms, Difference Equation

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Homework Statement


An LTI discrete-time system has frequency response given by
33bz3py.jpg


(a) Use one of the above forms of the frequency response to obtain an equation for the
impulse response h[n] of the system.

(b) From the frequency response, determine the difference equation that is satisfied by
the input x[n] and the output y[n] of the system.

(c) If the input to this system is
x[n]=4+2cos(won) for oo<n<oo,
for what value of wo will the output be of the form
y[n] =A constant
for -00 < n < oo? What is the constant A?


2. The attempt at a solution
(a) i found to be
h[n] = (0.8)^n u[n] + (0.8)^n-2 u[n-2]

Can anyone help me with the rest of the two parts?
 

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